`a)`
`4x^2 - 3x - 1`
`= 4x^2 - 4x + x - 1`
`= 4x(x - 1) + (x - 1)`
`= (4x + 1)(x - 1)`
`b)`
`4x^2 + 4x - 3`
`= 4x^2 + 4x + 1 - 4`
`= (2x + 1)^2 - 2^2`
`= (2x + 1 + 2)(2x + 1 - 2)`
`= (2x + 3)(2x - 1)`
`c)`
`2x^2 + 5x + 2`
`= 2x^2 + 4x + x + 2`
`= 2x(x + 2) + (x + 2)`
`= (2x + 1)(x + 2)`
`d)`
`6x^2 + 11x + 4`
`= 6x^2 + 3x + 8x + 4`
`= 3x(2x + 1) + 4(2x + 1)`
`= (3x + 4)(2x + 1)`
`e)`
`3x^2 - 5x - 2 `
`= 3x^2 + x - 6x - 2`
`= x(3x + 1) - 2(3x + 1)`
`= (x - 2)(3x + 1)`